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When
to Use an Individual-X / MR Chart
Individual-X / Moving Range
charts are generally used when you can't group measurements into rational
subgroups, when it's more convenient to monitor actual observations rather
than subgroup averages, or when the process distribution is very skewed
or bounded. Each subgroup, consisting of a single observation, represents
a "snapshot" of the process at a given point in time. The charts'
x-axes are time based, so that the charts show a history of the process.
For this reason, you must have data that is time-ordered; that is, entered
in the sequence from which it was generated. If this is not the case, then
trends or shifts in the process may not be detected, but instead attributed
to random (common cause) variation.
If rational subgroups
can be formed, the X-bar Charts are generally preferred, since the control
limits are easily calculated using the Normal distribution. (See Distributions
). When process distributions are bounded or skewed, or when Rational
Subgroups cannot be formed, then it is better to use an Individual-X
Chart. This, however, requires that we know the distribution of the process,
since this will define the statistical control limits.
Individual-X Charts are
efficient at detecting relatively large shifts in the process average, typically
shifts of +-3 sigma or larger. If X-bar charts can be used, then their larger
subgroups will detect smaller shifts. EWMA and Cu Sum charts can provide
higher sensitivity to smaller process shifts.
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